s/(\d{2})(\d{2})(\{2})/$3\.$2\.20$1/;

Are you sure you meant it that way? Also, you should get in the habit of treating years as numbers, not strings, although that's not likely to be a problem in this specific case.

s/(\d{2})(\d{2})(\d{2})/"$3.$2." . (2000 + $1)/e;
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Makeshifts last the longest.